Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions

Abstract

Hypergeometric functions provide a useful representation of Feynman diagrams occuring in precision phenomenology. In dimension regularization, the epsilon-expansion of these functions about d=4 is required. We discuss the current status of differential reduction algorithms. As an illustration, we consider the construction of the all-order epsilon-expansion of the Appell hypergeometric function about integer values of the parameters and present an explicit evaluations of the first few terms.

Comments: Poster presentation by S.A. Yost at the 34th International Conference on High Energy Physics, Philadelphia, August 2008. 3 pages, no figures, revtex4, slac_one.rtx. Version 4 corrects the arguments of one equation (between eqs. 5 and 6). Version 5 updates the template for ICHEP08